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Lubricated Flow of a Viscous Liquid in a Pipe

Mark J. McCready
Organization: University of Notre Dame
Department: Department of Chemical Engineering
URL: http://www.nd.edu/~mjm
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This notebook solves the "lubricated" flow in a pipe problem and in doing so demonstrates several major fundamental points in Transport Phenomena.

1. For flows where more than one fluid is flowing together, there is a separate equation for the velocity profile for each fluid. These equations differ just by the fluid properties.

2. To solve these two-fluid problems you need to recognize: The pressure drop is the same in each phase if gravity can be ignored. The velocity of the two fluids match at the interface. The shear stress in each fluid matches at the interface.

The last two of these are common boundary conditions.

For this specific situation the major results are:

Lubricated transport can cause a flow rate enhancement of the viscous fluid (compared to this fluid flowing alone in the pipe) on the order of the viscosity ratio of two fluids and the maximum enhancement occurs when the less viscous fluid occupies the outer 30% of the radius. Further, there is a range of flowrates where increasing the flow rate of the lubricating fluid, decreases the pressure drop!

*Science > Physics > Fluid Mechanics

Lubricated flow, Core-annular flow, Multifluid flow, Transport Phenomena example problem
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lubricatedflow.nb (718.7 KB) - Mathematica notebook